Question

Another Calculus question comin' atcha! Screenshot in the comments.

Answer 1

Any ideas from your last question?

Answer 2

Hint: fundamental theorem of calc
\[\frac{d}{dx}\int_c^{g(x)}f(t)~dt=f(g(x)) \times g'(x)\]

Answer 3

Are they related at all? would it be 2x(x^2^2)?

Answer 4

Not quite, with \(f(t)=t^t\), this makes \(f(g(x))=\big[g(x)\big]^{g(x)}\).

Answer 5

In this case, \(x^2\) is being raised to the power of \(x^2\), so you have
\[\big(x^2\big)^{x^2}=x^{2x^2}\]

Answer 6

Ok, it seems I got that part, 2x(x^2)x^2, so now I just plug in 3 for x?

Answer 7

Yup! I got the answer right. Thanks a bunch!

Answer 8

Yes, provided you have the right exponents and such

Answer 9

yw